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*DECK RFFTF1
SUBROUTINE RFFTF1 (N, C, CH, WA, IFAC)
C***BEGIN PROLOGUE RFFTF1
C***PURPOSE Compute the forward transform of a real, periodic sequence.
C***LIBRARY SLATEC (FFTPACK)
C***CATEGORY J1A1
C***TYPE SINGLE PRECISION (RFFTF1-S, CFFTF1-C)
C***KEYWORDS FFTPACK, FOURIER TRANSFORM
C***AUTHOR Swarztrauber, P. N., (NCAR)
C***DESCRIPTION
C
C Subroutine RFFTF1 computes the Fourier coefficients of a real
C periodic sequence (Fourier analysis). The transform is defined
C below at output parameter C.
C
C The arrays WA and IFAC which are used by subroutine RFFTB1 must be
C initialized by calling subroutine RFFTI1.
C
C Input Arguments
C
C N the length of the array R to be transformed. The method
C is most efficient when N is a product of small primes.
C N may change so long as different work arrays are provided.
C
C C a real array of length N which contains the sequence
C to be transformed.
C
C CH a real work array of length at least N.
C
C WA a real work array which must be dimensioned at least N.
C
C IFAC an integer work array which must be dimensioned at least 15.
C
C The WA and IFAC arrays must be initialized by calling
C subroutine RFFTI1, and different WA and IFAC arrays must be
C used for each different value of N. This initialization
C does not have to be repeated so long as N remains unchanged.
C Thus subsequent transforms can be obtained faster than the
C first. The same WA and IFAC arrays can be used by RFFTF1
C and RFFTB1.
C
C Output Argument
C
C C C(1) = the sum from I=1 to I=N of R(I)
C
C If N is even set L = N/2; if N is odd set L = (N+1)/2
C
C then for K = 2,...,L
C
C C(2*K-2) = the sum from I = 1 to I = N of
C
C C(I)*COS((K-1)*(I-1)*2*PI/N)
C
C C(2*K-1) = the sum from I = 1 to I = N of
C
C -C(I)*SIN((K-1)*(I-1)*2*PI/N)
C
C If N is even
C
C C(N) = the sum from I = 1 to I = N of
C
C (-1)**(I-1)*C(I)
C
C Notes: This transform is unnormalized since a call of RFFTF1
C followed by a call of RFFTB1 will multiply the input
C sequence by N.
C
C WA and IFAC contain initialization calculations which must
C not be destroyed between calls of subroutine RFFTF1 or
C RFFTB1.
C
C***REFERENCES P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
C Computations (G. Rodrigue, ed.), Academic Press,
C 1982, pp. 51-83.
C***ROUTINES CALLED RADF2, RADF3, RADF4, RADF5, RADFG
C***REVISION HISTORY (YYMMDD)
C 790601 DATE WRITTEN
C 830401 Modified to use SLATEC library source file format.
C 860115 Modified by Ron Boisvert to adhere to Fortran 77 by
C changing dummy array size declarations (1) to (*).
C 881128 Modified by Dick Valent to meet prologue standards.
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900131 Routine changed from subsidiary to user-callable. (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE RFFTF1
DIMENSION CH(*), C(*), WA(*), IFAC(*)
C***FIRST EXECUTABLE STATEMENT RFFTF1
NF = IFAC(2)
NA = 1
L2 = N
IW = N
DO 111 K1=1,NF
KH = NF-K1
IP = IFAC(KH+3)
L1 = L2/IP
IDO = N/L2
IDL1 = IDO*L1
IW = IW-(IP-1)*IDO
NA = 1-NA
IF (IP .NE. 4) GO TO 102
IX2 = IW+IDO
IX3 = IX2+IDO
IF (NA .NE. 0) GO TO 101
CALL RADF4 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3))
GO TO 110
101 CALL RADF4 (IDO,L1,CH,C,WA(IW),WA(IX2),WA(IX3))
GO TO 110
102 IF (IP .NE. 2) GO TO 104
IF (NA .NE. 0) GO TO 103
CALL RADF2 (IDO,L1,C,CH,WA(IW))
GO TO 110
103 CALL RADF2 (IDO,L1,CH,C,WA(IW))
GO TO 110
104 IF (IP .NE. 3) GO TO 106
IX2 = IW+IDO
IF (NA .NE. 0) GO TO 105
CALL RADF3 (IDO,L1,C,CH,WA(IW),WA(IX2))
GO TO 110
105 CALL RADF3 (IDO,L1,CH,C,WA(IW),WA(IX2))
GO TO 110
106 IF (IP .NE. 5) GO TO 108
IX2 = IW+IDO
IX3 = IX2+IDO
IX4 = IX3+IDO
IF (NA .NE. 0) GO TO 107
CALL RADF5 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4))
GO TO 110
107 CALL RADF5 (IDO,L1,CH,C,WA(IW),WA(IX2),WA(IX3),WA(IX4))
GO TO 110
108 IF (IDO .EQ. 1) NA = 1-NA
IF (NA .NE. 0) GO TO 109
CALL RADFG (IDO,IP,L1,IDL1,C,C,C,CH,CH,WA(IW))
NA = 1
GO TO 110
109 CALL RADFG (IDO,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW))
NA = 0
110 L2 = L1
111 CONTINUE
IF (NA .EQ. 1) RETURN
DO 112 I=1,N
C(I) = CH(I)
112 CONTINUE
RETURN
END
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